Details:
Title  Standard monomial theory for flag algebras of and  Author(s)  Sunyoung Kim  Type  Article in Journal  Abstract  Let G be the general linear group or the symplectic group over the complex numbers, and U be its maximal unipotent subgroup. We study standard monomial theory for the ring of regular functions on G / U , called the flag algebra, using the philosophy of Gröbner bases and SAGBI bases combined with classical invariant theory. From the realization of the flag algebra in a concrete polynomial setting, we obtain explicit standard monomial bases for irreducible representations. We also recreate known combinatorics of Young tableaux and Gelfand–Tsetlin patterns, and toric degenerations of flag varieties from the structure of leading monomials.  Keywords  Combinatorial representation theory, Classical groups, Young tableaux, Gelfand–Tsetlin patterns, Standard monomial theory, Toric degenerations, Flag algebras  ISSN  00218693 
URL 
http://www.sciencedirect.com/science/article/pii/S0021869308001142 
Language  English  Journal  Journal of Algebra  Volume  320  Number  2  Pages  534  568  Year  2008  Note  Computational Algebra  Edition  0  Translation 
No  Refereed 
No 
